Puzzle of the Day

These puzzles are also printed in Eight days a week, a booklet published by the Association of Teachers of Mathematics.

Start with any number and if it is even halve it but if it is odd add one. Now if this number is even halve it, if odd add one, and so on. Write each number down until you get to one. For instance 27 (add 1), 28 (halve it), 14 (halve it), 7 (add 1),8 (halve it), 4 (halve it), 2 (halve it),1 (stop). Which start number has the longest chain of numbers?

Answer: single digit is 9, 2-digit is 65, 3-digit is 513, 4-digit is 819